Question

Find an equation for the function f that has the given derivative and whose graph passes through the given point.
Derivative Point
f '(x) = 3 sin(9x) ( π/9 , − 14/3)

can someone please help me?

Answer 1

derivitive...f'(x)=3sin(9x)
Point....(pi/9,-14/3)

Answer 2

Methinks you're looking for something like this:
\[\int\limits3\times \sin(9x)dx\]
And then you have to tweak the constant so that it passes through the given point.

Answer 3

hmmm oki im still conffused could you work me through it?:S

Answer 4

i won't work you through the integration, i (my calculator) states that
\[\int 3 \times sin(9x)dx = -\frac{1}{3}cos(9x)+C\]
Now \[f(\frac{\pi}{9})=\frac{-14}{3}\]
\[-\frac{1}{3}cos(9\frac{\pi}{9})+C=\frac{-14}{3}\]
You should be able to continue from here on.

Answer 5

The solution is:
\[f(x)=-\frac{1}{3}cos(9x)-5\]

Answer 6

thank you so much this actually amkes sense..thanks...is it minus 5 its hard to read it

Answer 7

yes, -5, minus 5